The object of research. The research of interaction regularities of large-size reinforced concrete shells at the erection stages in heterogeneous soil mediums allowed to significantly expand the field of their rational use in underground construction for transport and engineering infrastructure facilities. For a defect-free erection of an underground structure of this type, it is necessary to solve the complex nonlinear design and geotechnical problems together. Method. Instability of interaction between a solid structure and ground environment, as well as the heterogeneity of the medium itself, generates a need to create an adaptive control stress-strain state of the system "gravitational large-size body - heterogeneous medium".  The geotechnical and structural calculations are used to simulate the interaction of the shell with the ground environment and to predict the adaptive stress-strain control system parameters. The adaptive stress-strain control methods provide conditions for a defect-free lifecycle of the structure during its erection and operation in complex soil and man-made conditions. Results. In contrast to the traditional approach, the paper proposes the foundations of a new concept for evaluating the interaction of large size sinking structures in differently resistant soils, taking into account the non-stationarity of the immersion mode.